The time of oscillation of a bar pendulum is shown to be practically unaffected by the use of a carriage supporting the knife-edge and sliding along the bar; the accuracy of the usual laboratory exercise on the bar pendulum is considerably increased. With a stop-watch showing tenths of a second the value of *g* can be determined quickly to within a few parts in 10,000.

If a flat, rigid body is pivoted about any point other than its center of mass and displaced by a small angle, the body will execute SHM (Simple Harmonic Motion).

Thederivation is similar to that of a simple pendulum since one can consider all the mass M to be located at the body's center of mass. Thena physical pendulum looks like a simple pendulum except that its moment of inertia is found using the parallel axis theorem.

_{}

**I _{cm}** =the body's moment of inertia about its center of mass.

h = Distance from pivot point to the center of mass.

M = Mass of the body.

Ifthe pivot joint is frictionless then the net torque acting on the planar object is given by the force of gravity perpendicular to lever arm, **Mg sin(q)**, times the length of the lever arm, **h:**

_{}

Whenthe angle of oscillation is small then the value of sin(q) and q or nearly the same provided q is measured in radians. Using this approximation, the above torque equation can be solved for the angular acceleration,

Since a =**d**^{2}q/**dt**^{2}, this equation is structurally similar to the differential equation for any type of SHM,

Matching terms with SHM equations,

and

_{.}

Here **w****'** is instantaneous angular velocity of the body while **w** is angular frequency of the body's SHM. They are not the same. Moreover, **w** is constant while **w****'** varies as the body oscillates back and forth.